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IEEE Transactions on Applied Superconductivity

1/f Noise Reduction With Noise Modulation in Time-Division Multiplexing

Kazuhiro Sakai, John Adams, Conjeepuram V. Ambarish, S. R. Bandler, James A. Chervenak, Tannaz Farrahi, Fred Michael Finkbeiner, Joshua D. Fuhrman, Samuel V. Hull, Richard L. Kelley, Caroline Anne Kilbourne, H. Muramatsu, F. S. Porter, S. J. Smith, Nicholas A. Wakeham, Edward J. Wassell

Published Jan 12, 2026• 0 citations
Publisher

Abstract

We present a novel noise modulation technique using SQUID gain switching for Time Division Multiplexing (TDM) readout systems that reduces 1/f noise by a factor of 3.5 while preserving the architectural simplicity that makes TDM a widely used technique for Transition Edge Sensor (TES) arrays. In contrast to frequency division multiplexing or microwave multiplexing, where signal modulation inherently provides immunity to low-frequency noise, conventional TDM systems can be susceptible to 1/f noise from downstream electronics as the TES signals remain in the low-frequency band. In our approach, the operating point of the SQUID amplifier alternates between positive and negative gain slopes at the frame frequency, combined with synchronized digital inversion of the error signals prior to flux-locked loop integration. This modulation scheme shifts the readout noise, including the 1/f components of low noise amplifiers, analog-to-digital converters and room temperature electronics, into the frame frequency range where it can be separated from the DC-TES signal by decimation filtering. Laboratory validation using an 8 column × 32 row TDM platform designed for Athena X-IFU applications shows a reduction in 1/f noise from 73 pA/√Hz@1Hz (9.3 μΦ₀/√Hz) to 21 pA/√Hz@1Hz (2.7 μΦ₀/√Hz) in channels with no TES connected, with the additional benefits of a 14-fold reduction in SQUID bias sensitivity through dynamic resistance matching and a 6.5-fold reduction in temperature-induced baseline drift. The technique avoids the disadvantage of doubling white noise, which occurs with conventional noise subtraction methods, and at the same time achieves a comparable suppression of 1/f noise. Implementation requires only minor firmware modifications to existing TDM systems, making it easily implementable for far-infrared bolometric and X-ray spectroscopy applications.

DOI
10.1109/tasc.2026.3652485

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Applied Physics Letters•Nov 1, 2021•4 citations
We present a novel noise modulation technique using SQUID gain switching for Time Division Multiplexing (TDM) readout systems that reduces 1/f noise by a factor of 3.5 while preserving the architectural simplicity that makes TDM a widely used technique for Transition Edge Sensor (TES) arrays. In contrast to frequency division multiplexing or microwave multiplexing, where signal modulation inherently provides immunity to low-frequency noise, conventional TDM systems can be susceptible to 1/f noise from downstream electronics as the TES signals remain in the low-frequency band. In our approach, the operating point of the SQUID amplifier alternates between positive and negative gain slopes at the frame frequency, combined with synchronized digital inversion of the error signals prior to flux-locked loop integration. This modulation scheme shifts the readout noise, including the 1/f components of low noise amplifiers, analog-to-digital converters and room temperature electronics, into the frame frequency range where it can be separated from the DC-TES signal by decimation filtering. Laboratory validation using an 8 column × 32 row TDM platform designed for Athena X-IFU applications shows a reduction in 1/f noise from 73 pA/√Hz@1Hz (9.3 μΦ₀/√Hz) to 21 pA/√Hz@1Hz (2.7 μΦ₀/√Hz) in channels with no TES connected, with the additional benefits of a 14-fold reduction in SQUID bias sensitivity through dynamic resistance matching and a 6.5-fold reduction in temperature-induced baseline drift. The technique avoids the disadvantage of doubling white noise, which occurs with conventional noise subtraction methods, and at the same time achieves a comparable suppression of 1/f noise. Implementation requires only minor firmware modifications to existing TDM systems, making it easily implementable for far-infrared bolometric and X-ray spectroscopy applications.
Abstract Transition-edge sensors (TESs) are sensitive devices for detecting photons from millimeter radiation to γ rays. Their photon counting efficiency and collecting area benefit from large-array multiplexing scheme, and therefore the development of multiplexing readout system has been an important topic in this field. Among the many multiplex techniques, time-division multiplexing (TDM) superconducting quantum interference device (SQUID) has been used most widely for TES readout. In this work, we design a Configurable Ultra-Low Noise Current Source (CLCS) for TES characterization and as a part of a whole TDM-TES bias control system. The CLCS is based on the feedback structure of ultra-low noise instrumentation amplifiers and low-noise, high-resolution (20 bits) digital-to-analog converter (DAC). CLCS has an ultra-high resolution of 10 nA in the 0 to 5 mA current output range, and can perform current-voltage (IV) sweep and bias-step tests to measure key TES parameters on board. The feedback structure of the CLCS also avoids the issue of impedance mismatch.
Time division multiplexing (TDM) developed for the Athena X-ray integral field unit (X-IFU) has achieved readout performance that can be scaled to multiplexing factors of several hundred for TES bolometer missions. The lower slew rate requirements of bolometer and soft X-ray missions favor greater first stage SQUID amplifier input mutual inductance (Min) to reduce readout noise and compensate for aliasing as multiplexing factor is increased. We find that, asMinincreases, TDM performance becomes sensitive to the design of the TES bias circuit, with degraded noise performance and the emergence of resonant features. In TDM chips with nanohenry scaleMin, we demonstrate that this sensitivity can be eliminated by adding intra-coil damping resistors to the superconducting transformers, enabling the robust use of these higherMinmultiplexers.
The frequency domain multiplexing (FDM) readout of arrays of transition edges sensors for the X-IFU/Athena and SAFARI/SPICA instruments requires SQUID amplifiers with low input inductance, low flux noise, high-dynamic range and low power consumption. We report the performance of two-stage SQUID amplifiers developed at VTT coupled to multiple high-Q LC resonators of the SRON FDM readout operating in the frequency range from 2 to 5 MHz. The SQUIDs have been tested in the following configurations: 1) the two SQUIDs at base temperature with open input; 2) the amplifier SQUID at 1K temperature and the front-end SQUID at base temperature in the FDM readout of low-G TES bolometers; and 3) and in the FDM readout of X-ray microcalorimeter arrays with both SQUIDS at base temperature. We measured an input flux noise equal to 0.18 μΦ0/Hz1/2at 20 mK, equivalent to an energy resolution of 9 b. The measured current noise at the SQUID input is ~1 pA/Hz1/2at 20 mK, which corresponds to a coupled energy resolution of about 15 b.
Dissipationless microwave radio frequency superconducting interference device (RF-SQUID) multiplexers are attractive for readouts of large format arrays of transition edge sensors (TES). This multiplexer has the potential for readout bandwidth of several GHz and power consumption of ≈0.1 pW per pixel, which are ≈103 and ≈10-4 times as large as those of DC-SQUID-based conventional multiplexers. To evaluate their readout performance for TES photon counters ranging from near infrared to gamma ray, white noise of this multiplexer was experimentally studied at 4 K. The reason for this was, firstly, to avoid the low-frequency fluctuation obvious at around 0.1 K but trivial for the energy resolution of photon counters, and secondly for a feasibility study of readout operation at 4 K for extended applications. To increase resonant Q at 4 K and maintain low-noise SQUID operation, multiplexer chips consisting of niobium nitride (NbN)-based coplanar-waveguide resonators and niobium (Nb)-based RF-SQUIDs have been developed. This hybrid multiplexer exhibited 1×104≤QI≤2×104 and the square root of spectral density of current noise referred to the SQUID input √SI =31 pA/√Hz, where QI is the internal Q of resonators. The former and the latter are factor-of-five and seven improvements from our previous results on Nb-based resonators, respectively. Systematic noise measurement with various microwave readout power PMR and two-directional readout on the complex plane of transmission component of scattering matrix S21 makes the contribution of each noise source obvious. By decreasing these noises to the degree achievable by current technology, we predicted the microwave RF-SQUID multiplexer would exhibit √SI ≤5 pA/√Hz; i.e., close to √SI of state-of-the-art DC-SQUID-based multiplexers.
Multiplexed superconducting quantum interference device (SQUID) readout systems are critical for measuring large arrays of superconducting transition-edge sensors (TES). We demonstrate a code-division SQUID multiplexing (CDM) architecture that is modulated by Walsh codes. Measurements and simulations of a prototype multiplexer show that this modulation scheme is not degraded by SQUID-noise aliasing, suppresses parasitic pickup, and has low levels of crosstalk. These properties enable this architecture to scale to large TES arrays. Furthermore, CDM modulation suppresses the 1/f knee in the noise to below 20 mHz, suggesting the use of this circuit for low-frequency-noise mitigation in more general SQUID applications.
We demonstrate multiplexing readout of 60 transition edge sensor (TES) bolometers operating at 90 mK using a frequency division multiplexing readout chain with bias frequencies ranging from 1 to 3.5 MHz and with a typical frequency spacing of 32 kHz. The readout chain starts with a two-stage SQUID amplifier and has a noise level of 9.5 pA/Hz. We compare current–voltage curves and noise spectra of TESs measured in a single-pixel mode and in a multiplexing mode. We also map the noise equivalent power (NEP) and the saturation power of the bolometers in both modes, where there are 43 pixels that do not show more than 10% difference in NEP and 5% in saturation power when measured in single pixel and multiplex modes. We have read out a TES with an NEP of 0.45 aW/Hz in the multiplexing-mode, which demonstrates the capability of reading out ultra-low noise TES bolometer arrays for space applications.